I am looking for a faithful translation of the (common in Australia) saying:

"If you throw enough shit against a wall, some of it has gotta stick."

It is in no way offensive, and means that if you try to attack a problem long enough and with enough varied methods, then eventually you must make some progress. A translation of this phrase would also need to have each of these properties to be faithful.

I find myself reaching for something similar at times when discussing my work. Is there an appropriate analogous saying in German, and if not, is there something close?

Please note there is a meta discussion relevant to this question here.

it loses the down-to-earth charm and the slight vulgarity of the Australian version, but I can't think of a way to properly transport that. Translating it literally ("Wenn man genug Scheiße an die Wand wirft..."), not being a known idiom, would be overly vulgar.

On second thought, a direct translation doesn't look that terrible IMO.
I would just remove the "shit". It would be a tad too vulgar for most audiences. So something like this: